An apparatus is provided for controlling a system to achieve a specified response. In one embodiment, the apparatus is a proportional, integrative, and derivative (PID) controller having a proportional element, an integrative element, and a derivative element coupled together. The elements respond to a reference signal and generate a control signal that causes a plant to generate a plant output. The proportional element has a gain element where the gain is a function of the ultimate gain of the plant (Ku) and the ultimate period of the plant (Tu). The controllers may also be embodied in non-PID controllers that share common elements, such as the use of: (a) Astrom-Hagglund controller output as an input for a subsequent controller; (b) internal feedback; and (c) a subsequent controller that performs a subtraction operation to generate the difference between the output of the Astrom-Hagglund controller and the output of the subsequent controller.
Legal claims defining the scope of protection, as filed with the USPTO.
1. A proportional, integrative, and derivative (PID) controller comprising a proportional element, an integrative element, and a derivative element coupled together and responsive to a reference signal to generate a control signal in response thereto to cause a plant to generate a plant output, wherein the proportional element has a gain element with a gain being substantially equal to 0.72 * K u * ⅇ - 1.6 K u + 1.2 K u 2 - .001234000198 * T u - 6.117274273 * 10 - 6 where K u is the ultimate gain of the plant and T u is the ultimate period of the plant.
2. The PID controller defined in claim 1 wherein gain on the integrative element is substantially equal to 0.72 * K u * e - 1.6 K u + 1.2 K u 2 0.59 * T u * e - 1.3 K u + 0.38 K u 2 - .06852522843250242 * K u T u .
3. The PID controller defined in claim 1 or 2 wherein gain on the derivative element is substantially equal to 0.108 * K u * T u * e - 1.6 K u + 1.2 K u 2 * e - 1.4 K u + 0.56 K u 2 - 0.002664037864 ( e T u ) log ( 1.634220701 log K u ) .
4. The PID controller defined in claims 1 or 2 wherein the reference signal is weighted by a weight substantially equal to 0.25 * e 0.56 K u + - 0.12 K u 2 + K u e K u before the plant output is subtracted therefrom and prior to being fed into the gain element associated with the proportional element.
5. A proportional, integrative, and derivative (PID) controller comprising a proportional element, an integrative element, and a derivative element coupled together and responsive to a reference signal to generate a control signal in response thereto to cause a plant to generate a plant output, wherein gain on the integrative element is substantially equal to 0.72 * K u * e - 1.6 K u + 1.2 K u 2 0.59 * T u * e - 1.3 K u + 0.38 K u 2 - .06852522843250242 * K u T u , where K u is the ultimate gain of the plant and T u is the ultimate period of the plant.
6. The PID controller defined in claim 5 wherein gain on the derivative element is substantially equal to 0.108 * K u * T u * e - 1.6 K u + 1.2 K u 2 * e - 1.4 K u + 0.56 K u 2 - 0.002664037864 ( e T u ) log ( 1.634220701 log K u ) .
7. The PID controller defined in claims 5 or 6 wherein the reference signal is weighted by a weight substantially equal to 0.25 * e 0.56 K u + - 0.12 K u 2 + K u e K u before the plant output is subtracted therefrom and prior to being fed into the gain element associated with the proportional element.
8. A proportional, integrative, and derivative (PID) controller comprising a proportional element, an integrative element, and a derivative element coupled together and responsive to a reference signal to generate a control signal in response thereto to cause a plant to generate a plant output, wherein the proportional element has a gain element with a gain being substantially equal to 0.72 * K u * ⅇ - 1.6 K u + 1.2 K u 2 - .001234000198 * T u - 6.117274273 * 10 - 6 where K u is the ultimate gain of the plant and T u is the ultimate period of the plant, and further wherein gain on the integrative element is substantially equal to 0.72 * K u * e - 1.6 K u + 1.2 K u 2 0.59 * T u * e - 1.3 K u + 0.38 K u 2 - .06852522843250242 * K u T u , gain on the derivative element is substantially equal to 0.108 * K u * T u * e - 1.6 K u + 1.2 K u 2 * e - 1.4 K u + 0.56 K u 2 - 0.002664037864 ( e T u ) log ( 1.634220701 log K u ) , and the reference signal is weighted by a weight substantially equal to 0.25 * e 0.56 K u + - 0.12 K u 2 + K u e K u before the plant output is subtracted therefrom and prior to being fed into the gain element associated with the proportional element.
9. A proportional, integrative, and derivative (PID) controller comprising a proportional element, an integrative element, and a derivative element coupled together and responsive to a reference signal to generate a control signal in response thereto to cause a plant to generate a plant output, the control signal being substantially the same to that produced by the controller having a proportional element, an integrative element, and a derivative element coupled together and responsive to a reference signal to generate a control signal in response thereto to cause a plant to generate a plant output, wherein the proportional element has a gain element with a gain being substantially equal to 0.72 * K u * ⅇ - 1.6 K u + 1.2 K u 2 - .001234000198 * T u - 6.117274273 * 10 - 6 where K u is the ultimate gain of the plant and T u is the ultimate period of the plant, and further wherein gain on the integrative element is substantially equal to 0.72 * K u * e - 1.6 K u + 1.2 K u 2 0.59 * T u * e - 1.3 K u + 0.38 K u 2 - .06852522843250242 * K u T u , gain on the derivative element is substantially equal to 0.108 * K u * T u * e - 1.6 K u + 1.2 K u 2 * e - 1.4 K u + 0.56 K u 2 - 0.002664037864 ( e T u ) log ( 1.634220701 log K u ) , and the reference signal is weighted by a weight substantially equal to 0.25 * e 0.56 K u + - 0.12 K u 2 + K u e K u before the plant output is subtracted therefrom and prior to being fed into the gain element associated with the proportional element.
10. A control apparatus comprising: an Astrom-Hagglund (A-H) controller operable to generate an A-H output; a subsequent controller operable in response to the A-H output to generate a control variable to control operation of a plant, wherein the subsequent controller comprises at least one lag element responsive to the A-H output.
11. The control apparatus defined in claim 10 wherein the subsequent controller comprises at least one input and is operable to generate a control variable that is used as feedback to the input, such that the subsequent controller has internal feedback.
12. The control apparatus defined in claim 10 wherein the subsequent controller comprises at least one input and has an internal feedback loop that provides a signal to the at least one input, the signal being other than an output of the subsequent controller.
13. The control apparatus defined in claim 10 wherein the subsequent controller comprises a subtractor to generate a difference between the A-H output and an output of the subsequent controller.
17. A control apparatus comprising: an Astrom-Hagglund (A-H) controller operable to generate an A-H output; a subsequent controller operable in response to the A-H output to generate a control variable to control operation of a plant, wherein the subsequent controller comprises at least one lead element responsive to the A-H output.
18. The control apparatus defined in claim 17 wherein the subsequent controller comprises at least one input and is operable to generate a control variable that is used as feedback to the input, such that the subsequent controller has internal feedback.
19. The control apparatus defined in claim 17 wherein the subsequent controller comprises at least one input and has an internal feedback loop that provides a signal to the at least one input, the signal being other than an output of the subsequent controller.
20. The control apparatus defined in claim 17 wherein the subsequent controller comprises a subtractor to generate a difference between the A-H output and an output of the subsequent controller.
24. A control apparatus comprising: an Astrom-Hagglund (A-H) controller operable to generate an A-H output; a subsequent controller operable in response to the A-H output to generate a control variable to control operation of a plant, wherein the subsequent controller comprises at least one input and is operable to generate a control variable that is used as feedback to the input, such that the subsequent controller has internal feedback.
25. The control apparatus defined in claim 24 wherein the subsequent controller comprises at least one input and is operable to generate a control variable that is used as feedback to the input, such that the subsequent controller has internal feedback.
26. The control apparatus defined in claim 24 wherein the subsequent controller comprises at least one input and has an internal feedback loop that provides a signal to the at least one input, the signal being other than an output of the subsequent controller.
30. A control apparatus comprising: an Astrom-Hagglund (A-H) controller operable to generate an A-H output; a subsequent controller operable in response to the A-H output to generate a control variable to control operation of a plant, wherein the subsequent controller comprises at least one input and has an internal feedback loop that provides a signal to the at least one input, the signal being other than an output of the subsequent controller.
31. The control apparatus defined in claim 30 wherein the subsequent controller comprises at least one input and is operable to generate a control variable that is used as feedback to the input, such that the subsequent controller has internal feedback.
32. The control apparatus defined in claim 30 wherein the subsequent controller comprises at least one input and has an internal feedback loop that provides a signal to the at least one input, the signal being other than an output of the subsequent controller.
36. A control apparatus comprising: an Astrom-Hagglund (A-H) controller operable to generate an A-H output; a subsequent controller operable in response to the A-H output to generate a control variable to control operation of a plant, wherein the subsequent controller comprises a subtractor to generate a difference between the A-H output and an output of the subsequent controller.
37. The control apparatus defined in claim 36 wherein the subsequent controller comprises at least one input and is operable to generate a control variable that is used as feedback to the input, such that the subsequent controller has internal feedback.
38. The control apparatus defined in claim 36 wherein the subsequent controller comprises at least one input and has an internal feedback loop that provides a signal to the at least one input, the signal being other than an output of the subsequent controller.
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July 12, 2002
January 25, 2005
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